Tesco Bank: 20,000 customers lose money
Alan Baxter from Berwick-upon-Tweed said he had lost £600, leaving him with just £21.88 in the bank.
He said: "Tesco said they couldn't offer me emergency funds but would offer £25 as a goodwill gesture.
"I've got food and petrol to pay for. I have a delivery of coal coming tomorrow for our coal-fired heater and I won't be able to pay."
Kevin Smith, from Blackpool, said he had lost £500 from one account and £20 from another.
He said: "I was just about to go to bed last night when I received a text message from Tesco saying there had been fraud on my account. So of course you panic."
Other customers complained on Tesco Bank's website and through social media about long delays when calling the company's customer service line to find out if their account was affected.
"Appalling service here. Woken at 4am to say contact urgently. Spent over three hours on hold. No answer," one wrote.
Another wrote: "Been waiting 40 mins to get through to @TescoBankNews. I hope my money is safe..."
A third said: "My weekend is not going very well, thanks to Tesco Bank. Money has vanished from my account and you don't even answer the phone."
Robert Schifreen, editor of the computer safety website Security Smart, said Tesco Bank must tell people what happened and how fraudsters obtained customers' bank details.
"It could be, for example, that people have been attaching skimming devices, card readers and cameras specifically to Tesco's cash point machines, so that they've been capturing people's accounts there," he told the BBC.
"It could be somebody who works at Tesco Bank who's had access to the database. It could be somebody else, who Tesco have passed information to, and that information has been hacked."
The Financial Conduct Authority says banks must refund unauthorised payments immediately, unless they have evidence that the customer was at fault or the payment was more than 13 months ago.
Banks are also required to refund any charges or interest added to your account as a result of the fraudulent payments.
Tesco Bank has been owned by Tesco plc since 2008, after starting as a joint venture with Royal Bank of Scotland.
The bank has more than seven million customer accounts and 4,000 staff, based in Edinburgh, Glasgow and Newcastle.